Optomechanical dynamics in the $\mathcal{PT}$- and broken-$\mathcal{PT}$-symmetric regimes

TL;DR

This paper provides a comprehensive theoretical analysis of optomechanical systems operating in $ ext{PT}$- and broken-$ ext{PT}$-symmetric regimes, revealing phase diagrams, control mechanisms, and dynamic behaviors of photons, phonons, and mechanical motion.

Contribution

It introduces a fully analytical framework for understanding the phase transitions and stability in $ ext{PT}$-symmetric optomechanical systems, enabling flexible control of their dynamical regimes.

Findings

Phase diagrams of optomechanical systems under $ ext{PT}$-symmetry.

Control of phase transitions via mechanical gain and optomechanical coupling.

Distinct dynamical behaviors in different $ ext{PT}$-regimes.

Abstract

We theoretically study the dynamics of typical optomechanical systems, consisting of a passive optical mode and an active mechanical mode, in the $\mathcal{PT}$- and broken-$\mathcal{PT}$-symmetric regimes. By fully analytical treatments for the dynamics of the average displacement and particle numbers, we reveal the phase diagram under different conditions and the various regimes of both $\mathcal{PT}$-symmetry and stability of the system. We find that by appropriately tuning either mechanical gain or optomechanical coupling, both phase transitions of the $\mathcal{PT}$-symmetry and stability of the system can be flexibly controlled. As a result, the dynamical behaviors of the average displacement, photons, and phonons are radically changed in different regimes. Our study shows that $\mathcal{PT}$-symmetric optomechanical devices can serve as a powerful tool for the manipulation of mechanical motion, photons, and phonons.